VELOCITY AND THE QUANTITY EQUATION
We can obtain another perspective on the quantity theory of money by considering the following question: How many times per year is the typical dollar bill used to pay for a newly produced good or service? The answer to this question is given by a variable called the velocity of money. In physics, the term velocity refers to the speed at which an object travels. In economics, the velocity of money refers .0 the speed at which the typical dollar bill travels around the economy from wallet to wallet.
To calculate the velocity of money, we divide the nominal value of output (nominal GDP) by the quantity of money. If P is the price level (the GDP defoliator), Y the quantity of output (real GDP), and M the quantity of money, then velocity is
P’= (P x Y)M.
To see why this makes sense, imagine a .simple economy that produces only pizza. Suppose that the economy produces 100 pizzas in a year, that a pizza sells for $10, and that the quantity of money in the economy is $50. Then the velocity of money is
V= ($’10 X-100)/$50
In this economy, people spend a total of $1,000 per’ year on pizza. For this $1,000 of spending to take place with only $50 of money, each dollar bill must change hands on average 20 time s per year. With slight algebraic rearrangement, this equation can be rewritten
M X V = P X Y
This equation states that the quantity of money (M) times the velocity of money (V) equals the price of output (P) times the amount of output (Y). It is called the quantity equation because it relates the quantity of money (M) to the nominal Value of output (P X Y). The quantity equation shows that an increase in the quantity of money in an economy must be reflected in one of the other three variables: Th e price level must rise, the quantity of output must rise, or the velocity of money must fall.